Sufficient conditions are obtained for the existence of multiple solutions to the
discrete fourth order periodic boundary value problem
\begin{equation*}
\begin{array}{l}
\Delta^4 u(t-2)-\Delta(p(t-1)\Delta u(t-1))+q(t) u(t)=f(t,u(t)),\quad t\in [1,N]_{\mathbb{Z}},\\
\Delta^iu(-1)=\Delta^iu(N-1),\quad i=0, 1,2, 3.
\end{array}
\end{equation*}
Our analysis is mainly based on the variational method and critical point theory.
One example is included to illustrate the result.